Modulation Instabilities in Birefringent Two-Core Optical Fibers

TL;DR

This paper analyzes how birefringence, cross-phase modulation, and polarization effects influence modulation instability in two-core optical fibers, revealing differences between birefringent and non-birefringent fibers in various dispersion regimes.

Contribution

It provides the first analysis of MI in birefringent two-core fibers considering polarization effects, with analytical solutions for asymmetric CW states and comparison to zero-birefringence fibers.

Findings

Asymmetric CW states exist above a power threshold sensitive to XPM.

In anomalous dispersion, MI gain spectra are similar to zero-birefringence fibers when scaled.

In normal dispersion, birefringence causes significant differences in MI spectra, especially in circular-birefringence fibers.

Abstract

Previous studies of the modulation instability (MI) of continuous waves (CWs) in a two-core fiber (TCF) did not consider effects caused by co-propagation of the two polarized modes in a TCF that possesses birefringence, such as cross-phase modulation (XPM), polarization-mode dispersion (PMD), and polarization-dependent coupling (PDC) between the cores. This paper reports an analysis of these effects on the MI by considering a linear-birefringence TCF and a circular-birefringence TCF, which feature different XPM coefficients. The analysis focuses on the MI of the asymmetric CW states in the TCFs, which have no counterparts in single-core fibers. We find that, the asymmetric CW state exists when its total power exceeds a threshold (minimum) value, which is sensitive to the value of the XPM coefficient. We consider, in particular, a class of asymmetric CW states that admit analytical solutions. In the anomalous dispersion regime, without taking the PMD and PDC into account, the MI gain spectra of the birefringent TCF, if scaled by the threshold power, are almost identical to those of the zero-birefringence TCF. However, in the normal dispersion regime, the power-scaled MI gain spectra of the birefringent TCFs are distinctly different from their zero-birefringence counterparts, and the difference is particularly significant for the circular-birefringence TCF, which takes a larger XPM coefficient. On the other hand, the PMD and PDC only exert weak effects on the MI gain spectra. We also simulate the nonlinear evolution of the MI of the CW inputs in the TCFs and obtain a good agreement with the analytical solutions.